Go to the ballet in the Royal Opera House. Plays seen: "The Nutcracker" and "Manon".

Tower Bridge Exhibition. Great views and interesting exhibition showing how the bridge opens.

Churchil Museum. Great way to appreciate one of the most famous British Prime Ministers.

Design Museum. Design through ages, not really worth it.

Museum in Docklands. Find out what was in Canary Wharf before it become the rich area that it is nowdays. There is also a display of pictures of the victims from Jack the Ripper. Not for the faint hearted.

The Household Cavalry Museum. See the royal horses in the heart of London. Cool videos of training and soldiers lifes.

Golden Hinde. A great place for everyone specially if you have an interest in old sailing ships.

The Cartoon Museum. Nothing very exciting apart from seeing hundreds of cartoons you've never heard of before.

Old Operating Theatre. Try doing it when they give a talk on how operations were held in the 1800 without pain killers. An extraordinary place full of life and things to touch.

Blackheath beer samples. Go in one of the pubs in Blackheath (sound London) and order the samples. You get a third of a pint of 5 different types of beer for 2 pounds. I sort of rather cheap night out.

Battersea Power Station. One of my favorites buildings in London. It is not particularly beautiful but it represents lots of things, at least for me. It is an incredibly big building that used to supply electricity 40 years ago. It got shut down and now it is just a massive empty shell. Pink Floyd used it in their album Animals to film a video of an inflatable pig flying over the 4 chimneys.

See a film (or even two) in the iMax cinema in the Science Museum. Huge screen and sort of cute, interesting films to watch. You may end up with a headache with all the 3D effects.

Battersea Dogs and Cats Home. A sad place in itself as there are plenty of stray animals waiting to be adopted. The cage sizes are ok, but still the animals become very stressed and some of them are quite scary.

Battersea Park. A quiet park to relax in and stroll around as it is not a touristy spot. Has some cool fountains and there is a nice path along the river.

Battersea Park Children's Zoo. Right in the heart of Battersea Park, they hold an egg treasure hunt over Easter. It hasn't got a massive display of exotic animals but it is well worth seeing as it is not too big and has enough variety to spend an afternoon.

Visit Richmond Park and see hundreds of deer. Fantastic experience to see those wild animals so close to the city.

London aquarium. Cool sharks and there is a place to touch Manta Rays.
Florence Nightingale museum. Interesting to see the evolution of modern nursery.
London Zoo.
HMS Belfast. A bit too big and long, but still interesting to know what people ate and how they lived in those ships.
Clink prison. Quite a big disappointment. Although there are some scare artifacts used to tortured people.
Natural history museum. Wonderful place to spend a whole day or just a couple of hours.
Imperial War museum. The main hall is very cool as it has real size planes hanging from the roof.
National portrait gallery. A lot of portraits...... although there is a 'portrait' of David Beckham which is basically a 5 minute video of him sleeping.
British library. You need to enroll in order to get access to most rooms but the free visitors room contains original papers written by Da Vinci and Nelson logs from battles.
British museum. Way too big. It could be a bit tedious and also is a great reminder of how little anyone knows. The mummies are the most interesting part.
Ceremony of the Keys in Tower of London. A way to get into the Tower of London for free. Also it is bizarre to think they still have the same ceremony to guard the queen keys. It has been around more than 700 years!!
Tower Bridge. A very deceiving building as it looks quite pathetic and tiny compared to the building around it but it is actually quite big and pretty.
Try to memorise the bridges from Vauxhall bridge to Tower bridge. This is particularly interesting when you are walking all along the south bank as most people haven't got a clue what bridge they cross to get to the north part of the river.
Buckingham palace. The statues in front of the palace are stunning. The palace itself has not much to see really, although St James Park is a very nice place to walk round.
Kensington gardens. Magnificent place to go back in history. Any time I go there I feel like I am in colonial Britain. Can't really understand why.
Albert memorial. A marvellous piece of art. One of my favourite status/monuments in the world.
Notting Hill carnival. This should be named Notting Hell carnival. Way too crowded. It is a nightmare to get there as most tube stations near the parade get closed, so half a million people try to get on the same tube to the only opened station. And when you actually survived the ride to get there, you will have to face the possibility of being squashed just to try to get a glimpse of the artist dancing.
Thames river carnival. Just a few weeks after the Nothing hill one but a lot less crowded and easier to enjoy. Still plenty of artist dancing and doing acrobatics. The Bolivian representation was quite impressive although a bit quiet compared with the loud Samba and rap displays.

Visit inside houses of parliament. Quite interesting to see the 'forbidden' place that you can only see on TV with the UK leaders arguing vividly.
Dali exhibition. An extraordinary collection well worth seeing. The sexual section could be a bit disturbing but nonetheless interesting.
Tate Modern. Imposing power station converted in a huge modern art gallery. A lot of enjoyable free exhibitions. A nice way to finish a walk round the south bank. The turbine hall is a unique place for artist as they get challenged to make a old factory huge room into an artistic attraction.
Tate Britain. Full of old art, it is an o.k. plan for a rainy sunday afternoon.
Madamme Tussauds. Impressive wax work although a bit tiring as it is basically trying to guess the next famous person in wax and take a photo with them.
London Eye. Amazing views of London, although it is more recommended when you actually know what the things you are looking at are.
South bank. Stroll along the south bank any afternoon. Pay attention to the human statues. This is my favourite one:
This is a blue classical guitar jukebox. Really nice songs interpreted in this rocky metallic blue fellow.

See a film in the National Film Theatre. There is usually an interesting variety of independent, weird, artistic films. Although be careful, the variety may not appeal to everyone as I saw some of the Bunuel early works and the people that went with me didn't seem very impressed.
Try to find a blue plaque. Quite hard to spot sometimes but it is nice when you find one as you know something happened right there. Something important.
Walk around Greenwich.
Walk through the wharfs and canals from tower bridge to Canary wharf. Quite nice to see all the different marinas and little yachts although it seems to never finish.
Canary Wharf. An interesting contrast between the usual sights of London and this borough fille completely with 20th century buildings an no trace of medieval London. Filled with skyscrapers that deploy light 24/7 its a scary place the financial area of London, where all the investment bankers run around like headless chicken in expensive suits.
Borough Market. For the food lovers, an indescribable set of colours, flavours and smells.
Portobello Market. Filled with different areas with food, clothes and antiques. As usual, lots of junk you don't need to buy.
Go to a medieval fair (in the summer, super cool). Not in London but possible to get to by train. It is really a cool experience, seeing people dressed in Medieval times, all the horse spectacles, hunting bird training. The highlights, wearing chainmail, helmet and sword and try to walk for more than 3 minutes. You will be suffocated an exhausted from the weight.
Escape to Southend for a day. This is real England. Hundreds of people being outside on a Saturday afternoon, enjoying some beer in the pub accompanied with fish and chips. It is also very close to the place where the Thames joins the sea, and the river is very shallow, so when the tide goes down it is possible to walk for for almost a kilometre where the retreating waters were.
Go up Monument. This is the candle like big column that you can actually go all the way up.
Camden town. Quite trendy and popular filled with alternative clothes markets and lots of fast food from all over the place. Crowded on Sundays with all sorts of people.

Eat bagels in Brick Lane. This is particularly good after having drank a few pints in the nice pubs. Although the selection of things that you can put in your bagel seems very dodgy.
Go out in Brick Lane. Very nice pubs to do out to there. However they closed down the main street at 1 am so it is quite disappointing not to be able stay till later and face the horrible trip back home so early.
Go out in old street. Lots of different types of clubs with a great atmosphere. Although coming back home, specially south London is a pain in the neck.
Soho.
Go to a musical. There are plenty of those to choose from. Try not to pay the ticket office prices as better prices can be found on the internet. I saw the We Will Rock you One. It was al right.
Go to the opera. I only saw the nutcracker and from the farthest seats you can ever get,but it is still a unique experience. The best of all is that you don't need to know anything about opera to enjoy it.
Golders Green. Visit the Jewish area of London where you can enjoy the delicacy of home made hummus and falafel. Also check out the time the shops open.
Check out Brixton. Quite a rough environment. The market offers a huge range of meat, poultry and fish with doubtful quality. Unfortunately I almost got beaten up in that market by a homeless woman who stole my phone.
go for a well cheap cinema entry in Peckham. Just 3 quid on Monday evenings!
Go to a gay club near Soho. It is a different way of going out to a club. Be prepared to be touched up by other men (if you are a man ).
Eat cheap pizza near Goodge Street. OK quality pizza that you can actually share between two people. Has seats and tables and its just nice.
Drink homemade beer near Goodge Street. The speciallity is the wheat beer which can be quite feeling. My personal selection is the cranberry beer wich tastes like cranberry juice and beer at the same time.
See the view from Hampstead Heath. An alternative place to check out the lights of London at night.
Go to one of the royal cemeteries. Or to be precise the Victorian cemeteries. One of them hosts the grave of Carl Marx.

Get lost in the centre of London and take the unusual routes, its surprising where you may end up.
Go out in Angel. Another cool place with plenty of pubs and clubs to enjoy.
Go for a pub gig in Earls Court. There are some nice pubs that held concerts by Bob Dylan, Beatles, Jimi Hendrix, Oasis and hundreds of artist. They are the cradle and hope for many new artists to become famous.
Go to a concert in Earls Court arena. The impressive thing is that people don't jump around like manics are shout things until they get a soar throat, even though they are allowed to drink.
Get tired of window shopping in Harrods. Remember this is not a place just for rich people, there are fairly ok priced items. I found a Pitaya there!! Although the price was way too much for one of those marvellous delicacies.

Be part of a TV show audience. You can get free tickets to different shows. It is interesting to see a filming studio, the whole set of cameras, lights and make up and more astonishingly the edited final product that you get.
Listen to a concert in the Barbican centre. Nice concert hall although very annoying to get to.
Have a beer next to the river in Chiswick
Watch the yearly Oxbridge boat race near Barnes Bridge. It is basically a lot of waiting jus to see two tiny boats approaching slowly followed by one dozen of security ships that create a huge set of waves.
Visit the city farms. This are fantastic places that house a great set of farm animals.

See the London whale skeleton. Its quite sad to think that lovely whale lost its way and found a grave in the Thames.
Take a boat cruise from Westminster to Greenwich.
Get hassled in the hundreds of Indian restaurants in Brick Lane. You can as a minimum get 25% discount on all food (not including dessert), first drink for free and they will let you bring your own wine.
Escape to Brighton for a day. Brighton is just a cool place to go, specially on a sunny summers day.
Escape to Cambridge for a day.
Escape to Oxford for a day.
Escape to Bournemouth for 2 days. Quote from Snatch : "We have sandy beaches".
Regents Park. This park is surrounded by a big complex of posh pretty buildings
BT tower foundations. There is a myth that says it is impossible to find the BT tower base...
Take a pottery class in New Cross Gate. Great way of explore new abilities and clumsiness with your hands. Also quite relaxing.
Take a life drawing class near Angel. Rediscover your childhood years trying to create exact copies of what you see in paper.
Ice skating in Canary Wharf. It is cool to do with all the huge buildings next to you. To think there are hundreds of people working in their offices on a Sunday evening making themselves richer than they need instead of just having a bit of fun.
Ice skating in the rain outside the National History Museum. Not very pleasant as it gets really slippery and damp, but the adrenalin can flow as you can get lots of speed due to the wet surface.
Get a cocktail in an ice glass in an Ice Bar. Pay to get cold in this really cool bar. Everything is made out of ice, the tables, chairs, bars, glasses.

Visit Little Venice. Nice set of water canals although the name really creates bigger expectations than it deserves.

Visit New Convent Garden market. Open on Sundays to the public is a big flea market full of stuff you probably don't need to buy. I received a leaflet for services regarding voodoo and spiritual support offered by experienced African priests.

Acknowledgments

The idea is to make a compilation of the so many things you can do in London. Quite a big number of them are free and other ones not that expensive. Many ideas were taken from the following sites:

www.londonforfree.net
www.londonfreelist.com
www.timeout.com/london

Some of them can be done in any city and other ones are not even in London but they are cool to put in there as they are kind of London based.